We present initial results from a new high-contrast imaging program dedicated to stars that exhibit long-term Doppler radial velocity accelerations ( or “ trends ” ) . The goal of the TRENDS ( T a R getting b EN chmark-objects with D oppler S pectroscopy and ) imaging survey is to directly detect and study the companions responsible for accelerating their host star . In this first paper of the series , we report the discovery of low-mass stellar companions orbiting HD 53665 , HD 68017 , and HD 71881 using NIRC2 adaptive optics ( AO ) observations at Keck . Follow-up imaging demonstrates association through common proper-motion . These co-moving companions have red colors with estimated spectral-types of K7–M0 , M5 , and M3–M4 respectively . We determine a firm lower-limit to their mass from Doppler and astrometric measurements . In the near future , it will be possible to construct three-dimensional orbits and calculate the dynamical mass of HD 68017 B and possibly HD 71881 B . We already detect astrometric orbital motion of HD 68017 B , which has a projected separation of 13.0 AU . Each companion is amenable to AO-assisted direct spectroscopy . Further , each companion orbits a solar-type star , making it possible to infer metallicity and age from the primary . Such benchmark objects are essential for testing theoretical models of cool dwarf atmospheres .